<i>Ab initio</i>study of electronic and magnetic properties of the C-codoped<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Ga</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi mathvariant="normal">Mn</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mi mathvariant="normal">N</mml:mi></mml:mrow></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mo>(</mml:mo><mml:mn>10</mml:mn><mml:mover accent="true"><mml:mn>1</mml:mn><mml:mo stretchy="false">¯</mml:mo></mml:mover><mml:mn>0</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math>surface

First principles calculations based on gradient corrected density functional theory have been carried out to study the magnetic coupling between Mn atoms in pure and carbon doped ${\mathrm{Ga}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}\mathrm{N}$ thin films. We show that the ground state of Mn-doped GaN $(10\overline{1}0)$ thin film, with Mn replacing the Ga sites, is antiferromagnetic but becomes ferromagnetic when it is codoped with C. The interaction between the Mn spins via the delocalized holes introduced by codoping of C at N sites is responsible for this transition. The overlap between Mn $3d$ and C $2p$ in the spin-up band renders half-metallic character to the C codoped (Ga,Mn)N system. The observed ferromagnetism in (Ga,Mn)N thin films is believed to be associated with defects or codoping with other elements during the film growth. The present study provides the theoretical understanding for many recent experiments on the Mn-doped GaN system.

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